Optimum Steady-State Position and Velocity Estimation Using Noisy Sampled Position Data

The Kalman filtering technique is used to obtain analytical expressions for the optimum position and velocity accuracy that can be achieved in a navigation system that measures position at uniform sampling intervals of T seconds through random noise with an rms value of ?x. A one-dimensional dynamic model, with piecewise-constant acceleration assumed, is used in the analysis, in which analytic expressions for position and velocity accuracy (mean square), before and after observations, are obtained. The errors are maximum immediately before position measurements are made. The maximum position error, however, can be bounded by the inherent sensor error by use of a sufficiently high sampling rate, which depends on the sensor accuracy and acceleration level. The steady-state Kalman filter for realizing the optimum estimates consists of a double integrator, the initial conditions of which are reset at each observation.